Some New Perspectives on Odd Sequential Graphs

Abstract

A graph $G=(V(G),E(G))$ with $p$ vertices and $q$ edges is said to be an \textit{odd sequential graph} if there is an injection $f:V(G)\rightarrow\{0,1,\ldots,q\}$ or if $G$ is a tree then $f$ is an injection $f:V(G)\rightarrow\{0,1,\ldots,2q-1\}$ such that when each edge $xy$ is assigned the label $f(x)+f(y)$, the resulting edge labels are $\{1,3,...,2q-1\}$. In this paper we investigate some new families of odd sequential graphs. We also introduce two new concepts namely bi-odd sequential graphs and global odd sequential graphs and some of their characteristics are discussed.